Potential theory associated with the Dunkl Laplacian

2015/11/12 by Hassine, Kods
#31B05 #31C40 #35J08 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.06638

Abstract

The main goal of this paper is to give potential theoretical approach to study the Dunkl Laplacian Δ_k which is a standard example of differential-difference operators. By introducing the Green kernel relative to Δ_k, we prove that the Dunkl Laplacian generates a balayage space and we investigate the associated family of harmonic measures. Therefore, by mean of harmonic kernels, we give a characterization of all Δ_k-harmonic functions on large class of open subsets U of ℝ^d. We also establish existence and uniqueness result of a solution of the corresponding Dirichlet problem.

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